**Numbers**

**Estimation**

The process of approximating or rounding off numbers to avoid complicated calculations is known as
**Estimation.**

We will learn the following types estimations:

- Rounding off/Estimation of numbers
- Estimating Sum
- Estimating Difference
- Estimating Product
- Estimating Quotient

**Rounding off/Estimation of numbers:**

**Rounding off to the nearest tens:**

- If the number has 1, 2, 3, or 4 at its unit place, round down the number.
- If the number has 5, 6, 7, 8, or 9 at its unit place, round up the number.
- To round off any number nearer to the tens, just consider its last two digits, that is. tens place and unit place digits.

**Example:**

**Question:** Round off 24836 to its nearest tens.

**Answer:** Here, the last two digits of 2483__6__ are ⟶ 3 and 6.

At the unit place, the number is 6. So, we need to **round up** the number.

Replace the number 36 by 40.

The number 36 is nearest to 40 than 30.

**So, 248 36 rounded to nearest tens is 24840.**

Following are some examples of rounding off to the nearest ten:

46__22__ ⟶ 46__20__ 266__55__ ⟶ 266__60__
6376__49__ ⟶ 6376__50__

**Rounding off to the nearest hundreds:**

- If the number has 0, 1, 2, 3 or 4 at its tens place, round down the number.
- If the number has 5, 6, 7, 8 or 9 at its tens place, round up the number.
- To round off any number nearest to the hundreds, just consider its last three digits, that is. hundred place, tens place and unit place digits.

**Example:**

**Question:** Round off 24836 to the nearest hundred.

**Answer:** Here, the last three digits of 24__836__ are ⟶ 836.

Tens place has number 3. So, we need to round down the number.

Replace the number 836 by 800.

Before 836 the nearest hundred number is 800.

**So, 24 836 rounded to the nearest hundred is 24800**

Some more examples of rounding off to the nearest hundred are:

4__622__ ⟶ 4__600__ 26__655__ ⟶ 26__700__
637__649__ ⟶ 637__600__

**Rounding off to the nearest thousand:**

- If the number has 0, 1, 2, 3 or 4 at its hundreds place, round down the number.
- If the number has 5, 6, 7, 8 or 9 at its hundreds place, round up the number.
- To round off any number to its nearest thousands, just consider its last four digits, i.e., thousands place, hundreds place, tens place, and units place numbers.

**Example:**

**Question:** Round off 24836 to its nearest thousand.

**Answer:** Here, the last four digits are 2__4836__ ⟶ 4836.

Hundreds place has number 8. So, we need to round up the number.

Replace the number 4836 by 5000.

After 4836 the nearest thousand number is 5000.

**So, 2 4836 rounded to the nearest thousand is 25000.**

Some more examples of rounding off to the nearest thousand are:

__4622__ ⟶ __5000__ 2__6655__ ⟶ 2__7000__
63__7649__ ⟶ 63__8000__

So, we get:

- 24836 rounded to the nearest tens is
**24840**. - 24836 rounded to the nearest hundred is
**24800**. - 24836 rounded to the nearest thousand is
**25000**.

**Estimating Sum or Difference**

- To estimate sum or difference, first we need to round off addends/minuend and subtrahend.
- Rounded off each number to the appropriate place of smaller addends.
- Rounded off each number to the appropriate place according to the subtrahend.

**Example:**

**Question 1:** Estimate the sum 15,835 + 4,573.

**Answer:**

**Step 1: Identify a smaller number.**

15,835 > 4,573 ⟶ (smaller number has 4-digits)

**Step 2: Rounding off each number to the nearest hundred.**

15,835 Rounds off to ⟶ 15,800

4,573 rounds off to ⟶ 4,600

**Step 3: Add.**

So, estimated sum is 15,800 + 4,600 = **20,400**

**Check estimated answer:**

Add the original numbers:

If we round off the original sum to the nearest hundreds, we get: **20,400**.

If we rounded off addends to the nearest tens, we get a more appropriate estimation but the calculation will not be as quick.

**Question 2:** Estimate: 24,782 − 3,669.

**Answer:**

**Step 1:** Subtrahend has 4-digits

24,782 > 3,669

**Step 2: Rounding off each number to the nearest hundred.**

24,782 Rounds off to ⟶ 24,800

3,669 rounds off to ⟶ 3,700

**Step 3: Subtract.**

So, estimated difference is 24,800 − 3,700 = **21,100**

**Check estimated answer:**

Subtract original numbers:

If we round off the original difference to the nearest hundreds, we **21,100**.

**Estimating Product**

To make multiplication easy, round off each number to its greatest place.

**Example:**

**Question:** Estimate: 3,781 × 295

**Answer:**

**Step 1: Round off each factor to its greatest place.**

3,781 Round off to thousands ⟶ 4,000

295 Round off to hundreds ⟶ 300

**Step 2: Multiply**

So, estimated product is 4,000 Ă— 300 = **12,00,000**

**Check estimated answer:**

Multiply the original numbers:

**Estimating Quotient**

To make division easy, round off the numbers to the same place.

**Example:**

**Question:** Estimate: 5,875 Ă· 697

**Answer:** Round off the number to the nearest thousand.

5,875 Round off to ⟶ 6,000

697 Round off to ⟶ 1,000

Now, divide.

**Check estimated answer:**

Divide the original numbers.

**Use of estimation in real life**

- To quickly guess the answer of the calculation between larger numbers.
- Estimation helps us to save time.
- Estimation helps us to save money.
- Estimation is used in various industries such as news, social media, weather department, share market, etc.